A surface is tame if its complement is ULC
Author:
R. H. Bing
Journal:
Trans. Amer. Math. Soc. 101 (1961), 294305
MSC:
Primary 54.75
MathSciNet review:
0131265
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
 [1]
J. W. Alexander, An example of a simply connected surface bounding a region which is not simply connected, Proc. Nat. Acad. Sci. U.S.A. vol. 10 (1924) pp. 810.
 [2]
R.
H. Bing, Locally tame sets are tame, Ann. of Math. (2)
59 (1954), 145–158. MR 0061377
(15,816d)
 [3]
, Approximating surfaces with polyhedral ones, Ann. of Math. vol. 61 (1957) pp. 456483.
 [4]
R.
H. Bing, An alternative proof that 3manifolds can be
triangulated, Ann. of Math. (2) 69 (1959),
37–65. MR
0100841 (20 #7269)
 [5]
R.
H. Bing, Conditions under which a surface in 𝐸³ is
tame, Fund. Math. 47 (1959), 105–139. MR 0107229
(21 #5954)
 [6]
, A wild sphere each of whose arcs is tame, Duke Math. J.
 [7]
, Side approximations of 2spheres, submitted to Annals of Math.
 [8]
Ralph
H. Fox and Emil
Artin, Some wild cells and spheres in threedimensional space,
Ann. of Math. (2) 49 (1948), 979–990. MR 0027512
(10,317g)
 [9]
Edwin
E. Moise, Affine structures in 3manifolds. IV. Piecewise linear
approximations of homeomorphisms, Ann. of Math. (2)
55 (1952), 215–222. MR 0046644
(13,765c)
 [10]
Edwin
E. Moise, Affine structures in 3manifolds. VIII. Invariance of the
knottypes; local tame imbedding, Ann. of Math. (2)
59 (1954), 159–170. MR 0061822
(15,889g)
 [11]
C.
D. Papakyriakopoulos, On Dehn’s lemma and the asphericity of
knots, Ann. of Math. (2) 66 (1957), 1–26. MR 0090053
(19,761a)
 [12]
John
R. Stallings, Uncountably many wild disks, Ann. of Math. (2)
71 (1960), 185–186. MR 0111003
(22 #1871)
 [1]
 J. W. Alexander, An example of a simply connected surface bounding a region which is not simply connected, Proc. Nat. Acad. Sci. U.S.A. vol. 10 (1924) pp. 810.
 [2]
 R. H. Bing, Locally tame sets are tame, Ann. of Math. vol. 59 (1954) pp. 145158. MR 0061377 (15:816d)
 [3]
 , Approximating surfaces with polyhedral ones, Ann. of Math. vol. 61 (1957) pp. 456483.
 [4]
 , An alternative proof that 3manifolds can be triangulated, Ann. of Math. vol. 69 (1959) pp. 3765. MR 0100841 (20:7269)
 [5]
 , Conditions under which a surface in is tame, Fund. Math. vol. 47 (1959) pp. 105139. MR 0107229 (21:5954)
 [6]
 , A wild sphere each of whose arcs is tame, Duke Math. J.
 [7]
 , Side approximations of 2spheres, submitted to Annals of Math.
 [8]
 R. H. Fox and E. Artin, Some wild cells and spheres in threedimensional space, Ann. of Math. vol. 49 (1948) pp. 979990. MR 0027512 (10:317g)
 [9]
 E. E. Moise, Affine structures in 3manifolds. IV. Piecewise linear approximations of homeomorphisms, Ann. of Math. vol. 55 (1952) pp. 215222. MR 0046644 (13:765c)
 [10]
 , Affine structures in 3manifolds, VIII. Invariance of the knottype; local tame imbedding, Ann. of Math. vol. 59 (1954) pp. 159170. MR 0061822 (15:889g)
 [11]
 C. D. Papakyriokopoulos, On Dehn's lemma and the asphericity of knots, Ann. of Math. vol. 66 (1957) pp. 126. MR 0090053 (19:761a)
 [12]
 J. R. Stallings, Uncountably many wild disks, Ann. of Math. vol. 71 (1960) pp. 185186. MR 0111003 (22:1871)
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC:
54.75
Retrieve articles in all journals
with MSC:
54.75
Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947196101312651
PII:
S 00029947(1961)01312651
Article copyright:
© Copyright 1961
American Mathematical Society
